Electrostatic Potential and Capacitance

Choose the wrong statement about equipotential surfaces.

• It is a surface over which the potential is constant

• The electric field is parallel to the equipotential surface

• The electric field is perpendicular to the equipotential surface

• The electric field is in the direction of steepest decrease of potential

Three capacitors connected in series have an effective capacitance of 4 µF. If one of the capacitance is removed, the net capacitance of the capacitor increases to 6 µF. The removed capacitor has a capacitance of

• 2 µF

• 4 µF

• 10 µF

• 12 µF

The electric potential V at any point (x, y, z) in space is given by V = 3x² where x, y, z are all in metre. The electric field at the point (1 m, 0, 2 m) is

• 6 V m^-1  along negative x-axis 

• 6 V m^-1  along positive x-axis 

• 12 V m^-1  along negative x-axis 

• 12 V m^-1 along positive x-axis 

Two equal point charges each of 3 µC are separated by a certain distance in metres. If they are located at (i + j + k)and (2i + 3j + k), then the electrostatic force between them is

• 9 × 10³ N

• 9 × 10^-3 N

• 16.5 × 10^-3 N

• 3 × 10^-3 N

Two resistors of resistances 200 kΩ and 1 MΩ respectively form a potential divider with outer junctions maintained at potentials of+ 3 V and −15 V. Then, the potential at the junction between the resistors is

• + 1 V

• − 0.6 V

• Zero

• − 12 V

Three capacitors are connected in the arms of a triangle ABC as shown in figure. 5 V is applied between A and B. The voltage between B and C is

• 2 V

• 1 V

• 3 V

• 1.5 V

Two point charges + 5 µC and − 2 µC are kept at a distance of 1 m in free space. The distance between the two zero potential points on the line joining the charges is

• $\frac{2}{7} \mathrm{m}$

• $\frac{2}{3} \mathrm{m}$

• $\frac{22}{21} \mathrm{m}$

• $\frac{20}{21} \mathrm{m}$

C,V,U and Q are capacitance, potential difference, energy stored and charge of a parallel plate capacitor respectively. The quantities that increase when a dielectric slab is introduced between the plates without disconnecting the battery are

• V and C

• V and U

• U and Q

• V and Q

A capacitor of capacitance value 1 µF is charged to 30 V and the battery is then disconnected. If the remaining circuit is connected across a 2 µF capacitor, the energy lost by the system is

• 300 µJ

• 450 µJ

• 225 µJ

• 150 µJ

Three charges Q₀, -q and -q are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if Q₀ is equal to

• $\frac{\mathrm{q}}{4}$

• $\frac{2\mathrm{q}}{\sqrt{32}}$

• $\sqrt{2\mathrm{q}}$

• + q